The superposition principle for local 1-dimensional currents
Metric Geometry
2025-03-25 v1 Analysis of PDEs
Functional Analysis
Abstract
We prove that every one-dimensional locally normal metric current, intended in the sense of U. Lang and S. Wenger, admits a nice integral representation through currents associated to (possibly unbounded) curves with locally finite length, generalizing the result shown by E. Paolini and E. Stepanov in the special case of Ambrosio-Kirchheim normal currents. Our result holds in Polish spaces, or more generally in complete metric spaces for 1-currents with tight support.
Keywords
Cite
@article{arxiv.2503.18157,
title = {The superposition principle for local 1-dimensional currents},
author = {Luigi Ambrosio and Federico Renzi and Federico Vitillaro},
journal= {arXiv preprint arXiv:2503.18157},
year = {2025}
}